Nonlinear elasticity.ipynb

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    "# Nonlinear elasticity\n",
    "In this chapter we investigate a nonlinear model of elastic strain in heterogeneous materials.  This system is equivalent to the $p$-system of gas dynamics, although the stress-strain relation we will use here is very different from the pressure-density relation typically used in gas dynamics.  The equations we consider have been investigated numerically in [<cite data-cite=\"leveque2002\"><a href=\"riemann.html#leveque2002\">(LeVeque, 2002)<a></cite>,<cite data-cite=\"leveque2003\"><a href=\"riemann.html#leveque2003\">(LeVeque & Yong, 2003)<a></cite>,<cite data-cite=\"2012_ketchesonleveque_periodic\"><a href=\"riemann.html#2012_ketchesonleveque_periodic\">(Ketcheson & LeVeque, 2012)<a></cite>].\n",
    "\n",
    "The equations are\n",
    "\\begin{align}\n",
    "\\epsilon_t(x,t) - u_x(x,t) & = 0 \\\\\n",
    "(\\rho(x)u(x,t))_t - \\sigma(\\epsilon(x,t),x)_x & = 0.\n",
    "\\end{align}\n",
    "\n",
    "The first equation is a kinematic relation, while the second represents Newton's second law.  This is a nonlinear conservation law with spatially varying flux function, in which\n",
    "\\begin{align}\n",
    "q & = \\begin{bmatrix} \\epsilon \\\\ \\rho u \\end{bmatrix}, & f(q,x) & = \\begin{bmatrix} -{\\mathcal M}/\\rho(x) \\\\ -\\sigma(\\epsilon,x) \\end{bmatrix}\n",
    "\\end{align}\n",
    "\n",
    "Here $\\epsilon$ is the strain, $u$ is the velocity, $\\rho$ is the material density, $\\sigma$ is the stress,\n",
    "and ${\\mathcal M}=\\rho u$ is the momentum.  If we take a linear stress strain relationship $\\sigma(\\epsilon,x)=K(x)\\epsilon$, then this system is equivalent to the acoustics equations that we have\n",
    "studied previously.  Here we consider instead a quadratic stress:\n",
    "\n",
    "\\begin{align}\n",
    "\\sigma(\\epsilon,x) = K_1(x) \\epsilon + K_2(x) \\epsilon^2.\n",
    "\\end{align}\n",
    "\n",
    "We assume that the spatially-varying functions $\\rho, K_1, K_2$ are piecewise constant, taking values\n",
    "$(\\rho_l, K_{1l}, K_{2l})$ for $x<0$ and values $(\\rho_r, K_{1r}, K_{2r})$ for $x>0$."
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    "## Hyperbolic structure\n",
    "The flux jacobian is\n",
    "\\begin{align}\n",
    "f'(q) = \\begin{bmatrix} 0 & -1/\\rho(x) \\\\ -\\sigma_\\epsilon(\\epsilon,x) & 0 \\end{bmatrix},\n",
    "\\end{align}\n",
    "with eigenvalues (characteristic sound speeds)\n",
    "\\begin{align}\n",
    "\\lambda^\\pm(x) = \\pm \\sqrt{\\frac{\\sigma_\\epsilon(\\epsilon,x)}{\\rho(x)}} = \\pm c(\\epsilon, x).\n",
    "\\end{align}\n",
    "\n",
    "Here for the stress-strain relation we have chosen, $\\sigma_\\epsilon = K_1(x) + 2 K_2(x)\\epsilon$.\n",
    "\n",
    "It's also convenient to define the nonlinear impedance $Z(\\epsilon, x) = \\rho(x) c(\\epsilon,x)$.  Then the eigenvectors of the flux Jacobian are\n",
    "\\begin{align}\n",
    "R & = \\begin{bmatrix} 1 & 1 \\\\ Z & -Z \\end{bmatrix}.\n",
    "\\end{align}\n",
    "Both characteristic fields are genuinely nonlinear.  Furthermore, since the characteristic speeds each have a definite sign, this system does not admit transonic rarefactions."
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    "### Structure of the Riemann solution\n",
    "Based on the eigenstructure of the flux jacobian above, the Riemann solution will always include a left-going and a right-going wave, each of which may be a shock or rarefaction.  Furthermore, we will see that the jump in $\\rho$ and $K$ at $x=0$ induces a stationary wave there.  Thus the overall structure of the Riemann solution is:\n",
    "\n",
    "![](./figures/nonlinear_elasticity_riemann.png)"
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   "source": [
    "### Hugoniot loci\n",
    "From the Rankine-Hugoniot jump conditions for the system we obtain the 1-Hugoniot locus for a state $(\\epsilon^*_l, u^*_l)$ connected by a 1-shock to a state $(\\epsilon_l, u_l)$:\n",
    "\\begin{align}\n",
    "u^*_l & = u_l - \\left( \\frac{\\left(\\sigma_l(\\epsilon^*_l)-\\sigma_l(\\epsilon_l)\\right)(\\epsilon^*_l-\\epsilon_l)}{\\rho_l}  \\right)^{1/2}\n",
    "\\end{align}\n",
    "Here $\\sigma_l(\\epsilon)$ is shorthand for the stress relation in the left medium.\n",
    "Similarly, a state $(\\epsilon^*_r,u^*_r)$ that is connected by a 2-shock to a state $(\\epsilon_r, u_r)$ must satisfy\n",
    "\\begin{align}\n",
    "u^*_r & = u_r - \\left( \\frac{\\left(\\sigma_r(\\epsilon^*_r)-\\sigma_r(\\epsilon_r)\\right)(\\epsilon^*_r-\\epsilon_r)}{\\rho_r}  \\right)^{1/2}.\n",
    "\\end{align}"
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   "source": [
    "### Integral curves\n",
    "The integral curves can be found by writing $\\tilde{q}'(\\xi) = r^{1,2}(\\tilde{q}(\\xi))$ and integrating.  This leads to\n",
    "\\begin{align}\n",
    "u^*_l  & = u_l + \\frac{1}{3 K_{2l} \\sqrt{\\rho_l}} \\left( \\sigma_{l,\\epsilon}(\\epsilon^*_l)^{3/2} - \\sigma_{l,\\epsilon}(\\epsilon)^{3/2} \\right) \\\\\n",
    "u^*_r  & = u_r - \\frac{1}{3 K_{2r} \\sqrt{\\rho_r}} \\left( \\sigma_{r,\\epsilon}(\\epsilon^*_r)^{3/2} - \\sigma_{r,\\epsilon}(\\epsilon)^{3/2} \\right)\n",
    "\\end{align}\n",
    "Here $\\sigma_{l,\\epsilon}$ is the derivative of the stress function w.r.t $\\epsilon$ in the left medium."
   ]
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   "source": [
    "### The entropy condition\n",
    "For a 1-shock, we need that $\\lambda^-(\\epsilon_l,x<0) > \\lambda^-(\\epsilon^*_l,x<0$, which is equivalent to $\\epsilon^*_l>\\epsilon_l$.  Similarly, a 2-shock is entropy-satisfying if $\\epsilon^*_r > \\epsilon_r$."
   ]
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   "source": [
    "### Interface conditions\n",
    "Because the flux depends explicitly on $x$, we do not necessarily have continuity of $q$ at $x=0$; i.e. in general $q^*_l \\ne q^*_r$.  Instead, the flux must be continuous: $f(q^*_l)=f(q^*_r)$.  For the present system, this means that the stress and velocity must be continuous, which makes sense from a physical point of view.  If the velocity were not continuous, the material would fracture (or overlap itself).  Continuity of the stress is required by Newton's laws."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Structure of rarefaction waves\n",
    "For this system, the structure of a centered rarefaction wave can be determined very simply.  Since the characteristic velocity must be equal to $\\xi = x/t$ at each point along the wave, we have $\\xi = \\pm\\sqrt{\\sigma_\\epsilon/\\rho}$, or\n",
    "\\begin{align}\n",
    "\\xi^2 = \\frac{K_1 + 2K_2\\epsilon}{\\rho}\n",
    "\\end{align}\n",
    "which leads to $\\epsilon = (\\rho\\xi^2 - K_1)/(2K_2)$.  Once the value of $\\epsilon$ is known, $u$ can be determined using the integral curves above."
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from scipy.optimize import fsolve\n",
    "import matplotlib.pyplot as plt\n",
    "from utils import riemann_tools\n",
    "from ipywidgets import interact, widgets\n",
    "from clawpack import riemann\n",
    "from exact_solvers import nonlinear_elasticity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%load exact_solvers/nonlinear_elasticity.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "aux_l = np.array((1., 5., 1.))\n",
    "aux_r = np.array((1., 2., 1.))\n",
    "q_l = np.array([2.1, 0.])\n",
    "q_r = np.array([0.0, 0.])\n",
    "\n",
    "ex_states, ex_speeds, ex_reval = nonlinear_elasticity.exact_riemann_solution(q_l,q_r,aux_l,aux_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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EmjAFaLlf4eHhVFVV6f8rzdj9BmifezUQkaZl4MCBzvl0K1as4NSpU857wcHBLFq0iFat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\n9G0WpgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10caa8190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function = riemann_tools.make_plot_function(ex_states, ex_speeds, ex_reval, \n",
    "                                                 layout='vertical',conserved_variables=('Strain','Momentum'))\n",
    "interact(plot_function, t=widgets.FloatSlider(value=0.1,min=0,max=.9));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Yb4GNwAbXbWMMkClTJv773/8ybtw4IOFLctCgQTZAosvMmTOZMGECgYGBLFy4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\nAS6bOHsB6zutAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d8c7f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nonlinear_elasticity.phase_plane_plot(q_l, q_r, aux_l, aux_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approximate solution of the Riemann problem using $f$-waves\n",
    "The exact solver above requires a nonlinear iterative solver and is relatively expensive.  A very cheap approximate Riemann solver for this system was developed in <cite data-cite=\"leveque2002\"><a href=\"riemann.html#leveque2002\">(LeVeque, 2002)<a></cite> using the $f$-wave approach.  One simply assumes that both nonlinear waves are shocks, with speeds equal to the characteristic speeds of the left and right states:\n",
    "\\begin{align}\n",
    "s^1 & = - \\sqrt{\\frac{\\sigma_{\\epsilon,l}(\\epsilon_l)}{\\rho_l}} \\\\\n",
    "s^2 & = + \\sqrt{\\frac{\\sigma_{\\epsilon,r}(\\epsilon_r)}{\\rho_r}}.\n",
    "\\end{align}\n",
    "Meanwhile, the waves are obtained by decomposing the jump in the flux $f(q_r,x>0) - f(q_l,x<0)$ in terms of the eigenvectors of the flux jacobian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "States in Riemann solution:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\left[\\begin{matrix}2.1\\\\0.0\\end{matrix}\\right], \\quad \\left[\\begin{matrix}0.994697686865492\\\\-3.35254790740842\\end{matrix}\\right], \\quad \\left[\\begin{matrix}2.37060935958126\\\\-3.35254790740842\\end{matrix}\\right], \\quad \\left[\\begin{matrix}0.0\\\\0.0\\end{matrix}\\right]\\right ]$$"
      ],
      "text/plain": [
       "⎡⎡2.1⎤, ⎡0.994697686865492⎤, ⎡2.37060935958126 ⎤, ⎡0.0⎤⎤\n",
       "⎢⎢   ⎥  ⎢                 ⎥  ⎢                 ⎥  ⎢   ⎥⎥\n",
       "⎣⎣0.0⎦  ⎣-3.35254790740842⎦  ⎣-3.35254790740842⎦  ⎣0.0⎦⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Waves (jumps between states):\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\left[\\begin{matrix}-1.10530231313451\\\\-3.35254790740842\\end{matrix}\\right], \\quad \\left[\\begin{matrix}1.37591167271577\\\\0.0\\end{matrix}\\right], \\quad \\left[\\begin{matrix}-2.37060935958126\\\\3.35254790740842\\end{matrix}\\right]\\right ]$$"
      ],
      "text/plain": [
       "⎡⎡-1.10530231313451⎤, ⎡1.37591167271577⎤, ⎡-2.37060935958126⎤⎤\n",
       "⎢⎢                 ⎥  ⎢                ⎥  ⎢                 ⎥⎥\n",
       "⎣⎣-3.35254790740842⎦  ⎣      0.0       ⎦  ⎣3.35254790740842 ⎦⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Speeds: \n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}-3.03315017762062 & 0.0 & 1.4142135623731\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "[-3.03315017762062  0.0  1.4142135623731]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fluctuations amdq, apdq: \n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\left[\\begin{matrix}3.35254790740842 & 10.1687812808375\\end{matrix}\\right], \\quad \\left[\\begin{matrix}-3.35254790740842 & 4.74121871916252\\end{matrix}\\right]\\right ]$$"
      ],
      "text/plain": [
       "[[3.35254790740842  10.1687812808375], [-3.35254790740842  4.74121871916252]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solver = riemann.nonlinear_elasticity_1D_py.nonlinear_elasticity_1D\n",
    "\n",
    "problem_data = {'stress relation' : 'quadratic'}\n",
    "fwave_states, fwave_speeds, fwave_reval = riemann_tools.riemann_solution(solver,q_l,q_r,aux_l,aux_r,\n",
    "                                                             problem_data=problem_data,verbose=True,\n",
    "                                                             stationary_wave=True,fwave=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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//PADbdq04U9/+hPvvvtu0PEkBmRlZdGlSxc++ugjXnzxRS666KKgI4mUOSrQ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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cf52190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function = riemann_tools.make_plot_function(fwave_states,fwave_speeds, fwave_reval,\n",
    "                                                 layout='vertical', conserved_variables=('Strain','Momentum'))\n",
    "interact(plot_function, t=widgets.FloatSlider(value=0.1,min=0,max=.9,step=.1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparison of exact and approximate solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FhRUUU7lxHfPevXs5duwYw4YNo27dukXunTx5ki1bttCtWzfatGlT5F5+yG7YsGGxZ0sL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\nOF4JAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d3ca790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function = riemann_tools.make_plot_function([ex_states,fwave_states],\n",
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    "                                                 [ex_reval,fwave_reval],\n",
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